In Ñoldorin Tarquesta [TQ], the d vanished in the combinations ndy, ldy, rdy, resulting in ny, ly, ry in that dialect. When Tolkien first mentioned these combinations in the Outline of Phonetic Development (OP1) from the 1940s, he described only the Lindarin [pre-Vanyarin] phonetic developments, where he first had [ndj, ldj, rdj] develop into [ndʒ, ldʒ, rdʒ]:

In TQ, based on Lindarin pronunciation, ty was pronounced [tš]. dy in ndy, ldy, rdy was pronounced [dž]. Thus kwendya was pronounced quenja [kwendža]. But the sound [dž], which did not occur in N. or T., and in Q. only occurred in these not very common combinations, presented difficulties, and ... (OP1: PE19/46 note #98).

He never finished this sentence, immediately revising the phonetic developments to the one described above:

But dy in ndy, ldy, rdy (none of them very frequent) did not develop to the corresponding [dž] in Lindarin. In consequence ndy, ldy, rdy tended to be confused with ny, ly, ry already in late PQ; and this pronunciation (and also the simplified spelling) is normal in TQ. Hence TQ Quenya for early PQ kwendya (OP1: PE19/46).

In the 1950s he used both scenarios, but with [ndj, ldj, rdj] > [ndʒ, ldʒ, rdʒ] in Vanyarin and > [nj, lj, rj] in Ñoldorin, as discussed in the Outline of Phonology (OP2):

In Vanyarin, parallel to the pronunciation of ty as [tš], dy was pronounced [dž], as English “j”, and ndy and ny consequently remained quite distinct. In Noldorin, however, ndy > nny > ny became, in normally pronounced colloquial uninfluenced by the PQ spelling, identical with original ny. Similarly with ldy, rdy and ly, ry (OP2: PE19/98).

In the 1930s, the word ᴹQ. Quenya was the primary example of this sound change, but a few other appeared in The Etymologies:

• ᴹ√ÉNED > endya > ᴹQ. enya “middle” (Ety/ÉNED).
• ᴹ✶windı̯ā > ᴹQ. vinya “pale blue” (Ety/WIN).

In the OP2 notes mentioned above, Tolkien said that Q. Quenya was not actually an example of this sound change, because the pronunciation was Quenya in Vanyarin as well. But in linquistic notes from the late 1950s or early 1960s Tolkien said this word was derived from ✶kwend(i)ja (PE17/138), and in the Quendi and Eldar essay written around 1960 he said:

This is historically correct, whatever may be the ultimate etymology of Quenya before the Eldar came to Aman. The view taken above (p. 360) is that it is derived from an adjective *kwendjā formed upon the stem *kwende (of which *kwendi was the plural), meaning “belonging to the Quendi or Elves” (WJ/393).

In this same document he said the Vanyarin form remained Quendya but he did not indicate its exact pronunciation (WJ/361). Thus it seems Tolkien vacillated on the primitive form of the word Quenya and often had ✶kwendyā > (Ñ.) Quenya.

Conceptual Development: Based on the examples ᴱ✶dyen(d)ye(n) > ᴱQ. ’yenye(n) “yesterday” (QL/105) and ᴱ✶nindyā > ᴱQ. ninya “blue” (PE13/164), this sound change dates back to the Early Quenya of the 1910s and 1920s. In the earliest period, this analysis is complicated by the presence of primitive voiced palatal stop [ɟ] that Tolkien usually represented as dy, so it is hard to tell if there were distinct developments for [ndj] and [nɟ] (I suspected not). As a general rule, [ɟ] (dy) > [j] (y) so the reduction of ndy > ny is not especially surprising.